In building tires, the drum width of the tire building drum is an essential factor for deciding tire sizes. In order to build a number of tires different in size by only one tire building machine, it is required to adjust the drum width. For this adjustment of the drum width, there have been provided a wide variety of apparatus one of which comprises a plurality of arcuate base segments radially expansible to collectively define a cylindrical shape; a pair of arcuate side flanges mounted on each of the arcuate base segments in opposing and spaced relation with each other to be axially slidable toward and away from each other; and an arcuate spacer section mounted on each of the arcuate base segments between the arcuate side flanges to form a cylindrical outer surface and a certain drum width of the tire building drum. The conventional tire building drum can be collapsed when the tire is removed from the tire building drum after it has been built thereon. The spacer section of the conventional tire building drum is in zigzag engagement with the opposing side flanges to be arranged at a widthwisely central position. Within each of the side flanges is formed a T-shape cross-sectioned and axially extending slot in which is received a head portion of a bolt having a stem portion extended throughout the side flange and the base segment to be screwed with a nut. In this way, the spacer section and the side flanges are secured to the base segment. The nut is however positioned internally of the base segment so that it is extremely difficul to screw the nut with the stem portion of the bolt within the base segment since there are many parts such as links, a rotary shaft and the like within the base segments. The axial movement of the side flange can not be smoothly effected since the head portion of the bolt is engaged with the axially extending slot to prevent the side flange from smoothly being moved. In addition, the screwing operation of the nut within the base segment is time consuming and over-screwing of the nut causes the slot to be broken and deformed, thereby further preventing the smooth movement of the side flange.